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Simplifying (0.30x + 5)(x + 25) = 0.27 Reorder the terms: (5 + 0.30x)(x + 25) = 0.27 Reorder the terms: (5 + 0.30x)(25 + x) = 0.27 Multiply (5 + 0.30x) * (25 + x) (5(25 + x) + 0.30x * (25 + x)) = 0.27 ((25 * 5 + x * 5) + 0.30x * (25 + x)) = 0.27 ((125 + 5x) + 0.30x * (25 + x)) = 0.27 (125 + 5x + (25 * 0.30x + x * 0.30x)) = 0.27 (125 + 5x + (7.5x + 0.30x2)) = 0.27 Combine like terms: 5x + 7.5x = 12.5x (125 + 12.5x + 0.30x2) = 0.27 Solving 125 + 12.5x + 0.30x2 = 0.27 Solving for variable 'x'. Reorder the terms: 125 + -0.27 + 12.5x + 0.30x2 = 0.27 + -0.27 Combine like terms: 125 + -0.27 = 124.73 124.73 + 12.5x + 0.30x2 = 0.27 + -0.27 Combine like terms: 0.27 + -0.27 = 0.00 124.73 + 12.5x + 0.30x2 = 0.00 Begin completing the square. Divide all terms by 0.30 the coefficient of the squared term: Divide each side by '0.30'. 415.7666667 + 41.66666667x + x2 = 0 Move the constant term to the right: Add '-415.7666667' to each side of the equation. 415.7666667 + 41.66666667x + -415.7666667 + x2 = 0 + -415.7666667 Reorder the terms: 415.7666667 + -415.7666667 + 41.66666667x + x2 = 0 + -415.7666667 Combine like terms: 415.7666667 + -415.7666667 = 0.0000000 0.0000000 + 41.66666667x + x2 = 0 + -415.7666667 41.66666667x + x2 = 0 + -415.7666667 Combine like terms: 0 + -415.7666667 = -415.7666667 41.66666667x + x2 = -415.7666667 The x term is 41.66666667x. Take half its coefficient (20.83333334). Square it (434.0277781) and add it to both sides. Add '434.0277781' to each side of the equation. 41.66666667x + 434.0277781 + x2 = -415.7666667 + 434.0277781 Reorder the terms: 434.0277781 + 41.66666667x + x2 = -415.7666667 + 434.0277781 Combine like terms: -415.7666667 + 434.0277781 = 18.2611114 434.0277781 + 41.66666667x + x2 = 18.2611114 Factor a perfect square on the left side: (x + 20.83333334)(x + 20.83333334) = 18.2611114 Calculate the square root of the right side: 4.273302166 Break this problem into two subproblems by setting (x + 20.83333334) equal to 4.273302166 and -4.273302166.Subproblem 1
x + 20.83333334 = 4.273302166 Simplifying x + 20.83333334 = 4.273302166 Reorder the terms: 20.83333334 + x = 4.273302166 Solving 20.83333334 + x = 4.273302166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.83333334' to each side of the equation. 20.83333334 + -20.83333334 + x = 4.273302166 + -20.83333334 Combine like terms: 20.83333334 + -20.83333334 = 0.00000000 0.00000000 + x = 4.273302166 + -20.83333334 x = 4.273302166 + -20.83333334 Combine like terms: 4.273302166 + -20.83333334 = -16.560031174 x = -16.560031174 Simplifying x = -16.560031174Subproblem 2
x + 20.83333334 = -4.273302166 Simplifying x + 20.83333334 = -4.273302166 Reorder the terms: 20.83333334 + x = -4.273302166 Solving 20.83333334 + x = -4.273302166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.83333334' to each side of the equation. 20.83333334 + -20.83333334 + x = -4.273302166 + -20.83333334 Combine like terms: 20.83333334 + -20.83333334 = 0.00000000 0.00000000 + x = -4.273302166 + -20.83333334 x = -4.273302166 + -20.83333334 Combine like terms: -4.273302166 + -20.83333334 = -25.106635506 x = -25.106635506 Simplifying x = -25.106635506Solution
The solution to the problem is based on the solutions from the subproblems. x = {-16.560031174, -25.106635506}
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